Some geometry of de Sitter space

In this expository note, I present some basic geometric and twistor theoretic facts about de Sitter space leading up to a discussion of Penrose’s quasi-local mass construction for linear gravity theory in the de Sitter background. The corresponding results for Minkowski space and anti–de Sitter space are familiar and can be found in \cite{PR} or \cite{HT} for the former and \cite{KT} for the latter. Some of the formulas given here are also quite familiar, but some are thought to be new and it is convenient to have these facts collected in one place.